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Mathematics Curriculum Guide Two-Year Algebra 1B 2016-17 Page 1 of 5 Paramount Unified School District Educational Services Topic 7A: Polynomials & Factoring Transfer Goals 1) Demonstrate perseverance by making sense of a never-before-seen problem, developing a plan, and evaluating a strategy and solution. 2) Effectively communicate orally, in writing, and using models (e.g., concrete, representational, abstract) for a given purpose and audience. 3) Construct viable arguments and critique the reasoning of others using precise mathematical language. Standards Understandings Major Standards A-SSE Seeing Structure in Expressions Interpret the structure of expressions [Linear, exponential, and quadratic] 1. Interpret expressions that represent a quantity in terms of its context. ★ a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P 1 r n as the 2. product of P and a factor not depending on P. ★ Use the structure of an expression to identify ways to rewrite it. A-APR Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomials [Linear and quadratic] 1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Students will understand that… Equivalence: A single quantity may be represented by many different expressions. Monomials may be used to form larger expressions called polynomials. Monomials can be written as a product of two or more monomials. Polynomials can be added and subtracted. There are several ways to find the product of two binomials, including models, algebra, and tables. Similar to integers, polynomials are closed under the operations of addition, subtraction, and multiplication. Properties: All the facts of arithmetic and algebra follow from certain properties. The properties of real numbers can be used to multiply a monomial by a polynomial, a binomial by a trinomial, or to simplify the product of binomials. Knowledge Students will know… Vocabulary: monomial, binomial, trinomial, polynomial, standard form of a polynomial, degree of a polynomial, coefficient, Distributive Property, square of a binomial, product of a sum and difference Procedures for: Adding polynomials by combining like terms. Subtracting polynomials by adding the additive inverse of the polynomial being subtracted. Multiplying a monomial with a polynomial using the distributive property. Multiplying two binomials using the distributive property (FOIL). Using special rules to simplify the square of a binomial or the product of a sum and difference. Mathematics Topic 7A Overview Course: Two-Year Algebra 1B Timeframe: 4 weeks/22 days Start Date: November 9, 2016 Assessment Dates: December 15-16, 2016 Essential Questions Students will keep considering… Can two algebraic expressions that appear to be different be equivalent? How are the properties of real numbers related to polynomials? How do polynomials form a system that is analogous to integers? Skills Students will be skilled at and able to do the following… Applying the properties of real numbers to add, subtract, multiply, and factor polynomials. Use the Commutative and Associative Properties to manipulate polynomial expressions. Use the Distributive Property to multiply polynomials and factor polynomials. Page 2 of 5 Paramount Unified School District Educational Services Topic 7A: Polynomials & Factoring Essential Questions: Standards: A-SSE 1a, A-SSE 1B, A-SSE 2, A-APR 1 Can two algebraic expressions that appear to be different be equivalent? How are the properties of real numbers related to polynomials? How do polynomials form a system that is analogous to integers? Time 4 Days Focus Questions for Lessons Lesson/ Activity Lesson 8-1 Adding and Subtracting Polynomials (pp. 486-491) Focus Question(s): How do polynomials form a system that is SMP 1 ,2, 3, 4, 6 analogous to integers with respect to addition and subtraction? What is the rule for simplifying like terms when you are adding and subtracting polynomials? Lesson 8-2 Multiplying and Factoring (pp. 492-496) SMP 1, 2, 3, 4 Focus Question(s): How do polynomials form a system that is analogous to integers with respect to multiplication? How can the properties of real numbers be applied to multiplying a monomial to a polynomial? Timeframe: 4 weeks/22 days Start Date: November 9, 2016 Assessment Dates: December 15-16, 2016 Understandings Knowledge Monomials can be used to form larger expressions called polynomials. Polynomials can be added and subtracted. Similar to integers, polynomials are closed under the operations of addition and subtraction. Vocabulary: monomial, degree of a monomial, polynomial, standard form of a polynomial, degree of a polynomial, binomial, trinomial Inquiry Question: p. 485 Planning a Garden Plot 2 Days Mathematics Topic 7A Pacing Course: Two-Year Algebra 1B A monomial can be multiplied by a polynomial using the Distributive Property. Similar to integers, polynomials are closed under the operation of multiplication. Students will know… That polynomials can be classified by degrees and by the number of terms. The standard form of a polynomial. How to add and subtract polynomials. Vocabulary: monomial, polynomial, Distributive Property Skills Classify, add, and subtract polynomials. Simplify polynomial expressions. Resources Notes: Emphasize to students that their final answer must be written in standard form. Include an example where students have to find the perimeter of a figure. Problems to Emphasize: 8-1 Think About a Plan. CC Problems: p. 489-490 #7,41,43 Multiply a monomial by a polynomial using the Distributive Property. Problems to emphasize: Page: 495 #8, 35, 36, 41 Students will know… The Distributive Property. The appropriate rules of exponents that can be applied when multiplying a power to a polynomial. Inquiry Question: p. 492 Solve It! Page 3 of 5 Time 6 Days Lesson/ Activity Lesson 8-3 Multiplying Binomials (FOIL & with Trinomials) (pp. 498-503) SMP 1, 2, 3, 4, 7, 8 Day 1: Multiplying binomials Day 2: Multiplying binomials and trinomials Day 3: Quiz 2 Days Lesson 8-4 Multiplying Special Cases (pp. 504-509) SMP 1, 2, 3, 4, 7, 8 Focus Questions for Lessons Focus Question(s): How do polynomials form a system that is analogous to integers with respect to multiplication? What are the methods for multiplying two binomials? What do all of the methods have in common? Inquiry Question: p. 498 Solve It! Focus Question(s): How do polynomials form a system that is analogous to integers with respect to multiplication? How do you model the square of a binomial? How do you model the product of a sum and difference? Understandings There are several ways to find the product of two binomials, including models, algebra, and tables. The properties of real numbers can be used to multiply two binomials. Similar to integers, polynomials are closed under the operation of multiplication. There are special rules you can use to simplify the square of a binomial or the product of a sum and difference. Similar to integers, polynomials are closed under the operation of multiplication. Inquiry Question: p. 504 Solve It! Knowledge Vocabulary: binomial, trinomial Students will know… The procedures for using the Distributive Property to multiply polynomials. That multiplying polynomials using algebra tiles or with a table will result in the same expression as using the Distributive Property. Vocabulary: square of a binomial, product of a sum and difference Students will know… That the square of a binomial can be modeled Additional Resources Skills Multiply two binomials. Multiply a binomial by a trinomial. Notes: Include examples where students have to… Multiply binomials before adding or subtracting it to a polynomial. Find the area of a rectangle. Find the area of a shaded region. Problems to emphasize: Page: 501 and 502 # 5, 6, 42 Think About a Plan 8-3 P. 503 Apply What You’ve Learned Simplify square of a binomial using special rules. Simplify product of a sum and difference using special rules. Problems to emphasize: Page: 508 #50, 51, 54, 57 8-3 Think About a Plan a 2 2ab b2 or a 2 2ab b2 . using The product of a sum and difference can be modeled using a 2 b2 . Common Core Practices Instruction in the Standards for Mathematical Practices Use of Talk Moves Note-taking Use of Manipulatives Use of Technology Use of Real-world Scenarios Project-based Learning Thinking Maps Page 4 of 5 Time Lesson/ Activity Focus Questions for Lessons Understandings Knowledge 4 Days Unit 7A Review Use Textbook Resources and/or Teacher Created Items 4 Days Topic 7A Assessments (Created and provided by PUSD) Skills Additional Resources Common Core Practices Instruction in the Standards for Mathematical Practices Use of Talk Moves Note-taking Use of Manipulatives Use of Technology Use of Real-world Scenarios Project-based Learning Thinking Maps Page 5 of 5